Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
223 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 223 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#4131 | C2 | semidirect |
| 2. #11717330 | C2 | semidirect |
| 4. #11716851 | C2 | semidirect |
| 5. #11716744 | C2 | semidirect |
| 6. #11716740 | C2 | semidirect |
| 7. #11716731 | C2 | semidirect |
| 18. #87809 | C4 | semidirect |
| 19. C5×#687 | C4 | semidirect |
| 20. #87775 | C4 | semidirect |
| 21. #87774 | C4 | semidirect |
| 42. #4131 | D5 | semidirect |
| 83. #687 | AGL(1,𝔽5) | semidirect |
| 141. C52 | #443 | semidirect |
| 204. C5 | #65433 | semidirect |
| 205. C5 | #65736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4131 | 2 |
| #11717330 | 2 |
| #11717053 | 2 |
| #11716851 | 2 |
| #11716744 | 2 |
| #11716740 | 2 |
| #11716731 | 2 |
| #65736 | 5 |
| #65433 | 5 |